Special unipotent representations of real classical groups: construction and unitarity

Let G G be a real classical group (including the real metaplectic group). We consider a nilpotent adjoint orbit O ˇ \check {\mathcal O} of G ˇ \check G , the Langlands dual of G G (or the metaplectic Langlands dual of G G when G G is a real metaplectic group). We classify all special unipotent representations of G G attached to O ˇ \check {\mathcal O} , in the sense of Arthur and Adams-Barbasch-Vogan. When O ˇ \check {\mathcal O} has good parity in the sense of Mœglin, we construct all such representations of G G via the method of theta lifting. As a consequence of the construction and the classification, we conclude that all special unipotent representations of G G are unitarizable, as predicted by the Arthur-ABV conjecture. We also determine the precise structure of the associated cycles of special unipotent representations of G G . The paper is the second in a series of two papers on the classification of special unipotent representations of real classical groups.